Physical Sciences and Mathematics Commons^™

The Process Of Tracking In Mathematics In Box Elder School District, Megan Haramoto Bushnell

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Educational policymakers have used tracking to instruct students in a variety of subjects, including mathematics. Tracking, which has also been called ability grouping, is a process by which students in the same grade are placed into different classes based on academic ability. Few educators and sociologists have looked at the process by which students are placed in different mathematics tracks. The research design of this study focused on accumulating, evaluating, and reporting the understanding and observations of 12 teachers and 4 counselors as they discussed their knowledge and involvement in the mathematics placement procedures from the intermediate and middle school …

Darboux Integrability Of Wave Maps Into 2-Dimensional Riemannian Manifolds, Robert Ream

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The harmonic map equations can be represented geometrically as an exterior differential system (EDS), ε. Using this representation we study the harmonic maps from 2D Minkowski space into 2D Riemannian manifolds. These are also known as wave maps. In this case, E is invariant under conformal transformations of Minkowski space. The quotient of ε by these conformal transformations, E/G, is an s=0 hyperbolic system.

The main result of our study is that the prolonged EDS, ε^(k), is Darboux integrable if and only if the prolonged quotient EDS, ε^(k+1), is Darboux integrable. We also find invariants determining …